Model Uncertainty for Bilinear Hysteretic Systems

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

Resumé

In structural reliability analysis at least three types of uncertainty must be considered, namely physical uncertainty, statistical uncertainty, and model uncertainty (see e.g. Thoft·Christensen & Baker [1)). The physical uncertainty is usually modelled by a number of basic variables. The statistical uncertainty -due to lack of information can e.g. be taken into account by describing the variables by predictive density functions, Veneziano [2). In general, model uncertainty is the uncertainty connected with mathematical modelling of the physical reality. When structural reliability analysis is related to the concept of a failure surface (or limit state surface) in the n-dimensional basic variable space then model uncertainty is at least due to the neglected variables, the modelling of the failure surface and the computational technique used. A more precise definition is given in section 2, where some different methods to treat model uncertainty are described. In section 3 a new method based on subjectively modelled conditional density functions is presented. It is shown that in some special cases this method is equivalent to existing more simple methods. In the analysis of dynamically loaded structures it is often assumed that the loading and the response can be modelled by stationary stochastic processes. Further, it is assumed that the structures can be modelled by non-linear systems showing hysteresis. This non-linear behaviour is essential to the design procedure from an economic and reliability point of view. In section 4 it is shown how the probability of failure of a simple bilinear oscillator can be estimated and in section 5 it is demonstrated by numerical examples how model uncertainty can be included in the calculations.
OriginalsprogEngelsk
TitelSystem Modelling and Optimization : Proceedings of the 11th IFIP Conference
RedaktørerPalle Thoft-Christensen
Antal sider10
ForlagSpringer
Publikationsdato1984
Sider585-594
ISBN (Trykt)3-540-13185-X
StatusUdgivet - 1984
BegivenhedSystem Modelling and Optimization: IFIP - København, Danmark
Varighed: 25 jul. 198329 jul. 1983
Konferencens nummer: 11

Konference

KonferenceSystem Modelling and Optimization
Nummer11
LandDanmark
ByKøbenhavn
Periode25/07/198329/07/1983
NavnLecture Notes in Control and Information Sciences
Vol/bind59
ISSN0170-8643

Fingerprint

reliability analysis
stochasticity
hysteresis
modeling
method
economics
calculation
analysis

Emneord

  • Bilinear Hysteretic Systems
  • Structural Reliability
  • Physical Uncertainty
  • Statistical Uncertainty
  • Model Uncertainty

Citer dette

Sørensen, J. D., & Thoft-Christensen, P. (1984). Model Uncertainty for Bilinear Hysteretic Systems. I P. Thoft-Christensen (red.), System Modelling and Optimization : Proceedings of the 11th IFIP Conference (s. 585-594). Springer. Lecture Notes in Control and Information Sciences, Bind. 59
Sørensen, John Dalsgaard ; Thoft-Christensen, Palle. / Model Uncertainty for Bilinear Hysteretic Systems. System Modelling and Optimization : Proceedings of the 11th IFIP Conference. red. / Palle Thoft-Christensen. Springer, 1984. s. 585-594 (Lecture Notes in Control and Information Sciences, Bind 59).
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title = "Model Uncertainty for Bilinear Hysteretic Systems",
abstract = "In structural reliability analysis at least three types of uncertainty must be considered, namely physical uncertainty, statistical uncertainty, and model uncertainty (see e.g. Thoft·Christensen & Baker [1)). The physical uncertainty is usually modelled by a number of basic variables. The statistical uncertainty -due to lack of information can e.g. be taken into account by describing the variables by predictive density functions, Veneziano [2). In general, model uncertainty is the uncertainty connected with mathematical modelling of the physical reality. When structural reliability analysis is related to the concept of a failure surface (or limit state surface) in the n-dimensional basic variable space then model uncertainty is at least due to the neglected variables, the modelling of the failure surface and the computational technique used. A more precise definition is given in section 2, where some different methods to treat model uncertainty are described. In section 3 a new method based on subjectively modelled conditional density functions is presented. It is shown that in some special cases this method is equivalent to existing more simple methods. In the analysis of dynamically loaded structures it is often assumed that the loading and the response can be modelled by stationary stochastic processes. Further, it is assumed that the structures can be modelled by non-linear systems showing hysteresis. This non-linear behaviour is essential to the design procedure from an economic and reliability point of view. In section 4 it is shown how the probability of failure of a simple bilinear oscillator can be estimated and in section 5 it is demonstrated by numerical examples how model uncertainty can be included in the calculations.",
keywords = "Bilinear Hysteretic Systems, Structural Reliability, Physical Uncertainty, Statistical Uncertainty, Model Uncertainty, Bilinea Hysteretic Systems, Structural Reliability, Physical Uncertainty, Statistical Uncertainty, Model Uncertainty",
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year = "1984",
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Sørensen, JD & Thoft-Christensen, P 1984, Model Uncertainty for Bilinear Hysteretic Systems. i P Thoft-Christensen (red.), System Modelling and Optimization : Proceedings of the 11th IFIP Conference. Springer, Lecture Notes in Control and Information Sciences, bind 59, s. 585-594, System Modelling and Optimization, København, Danmark, 25/07/1983.

Model Uncertainty for Bilinear Hysteretic Systems. / Sørensen, John Dalsgaard; Thoft-Christensen, Palle.

System Modelling and Optimization : Proceedings of the 11th IFIP Conference. red. / Palle Thoft-Christensen. Springer, 1984. s. 585-594 (Lecture Notes in Control and Information Sciences, Bind 59).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

TY - GEN

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AU - Sørensen, John Dalsgaard

AU - Thoft-Christensen, Palle

PY - 1984

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N2 - In structural reliability analysis at least three types of uncertainty must be considered, namely physical uncertainty, statistical uncertainty, and model uncertainty (see e.g. Thoft·Christensen & Baker [1)). The physical uncertainty is usually modelled by a number of basic variables. The statistical uncertainty -due to lack of information can e.g. be taken into account by describing the variables by predictive density functions, Veneziano [2). In general, model uncertainty is the uncertainty connected with mathematical modelling of the physical reality. When structural reliability analysis is related to the concept of a failure surface (or limit state surface) in the n-dimensional basic variable space then model uncertainty is at least due to the neglected variables, the modelling of the failure surface and the computational technique used. A more precise definition is given in section 2, where some different methods to treat model uncertainty are described. In section 3 a new method based on subjectively modelled conditional density functions is presented. It is shown that in some special cases this method is equivalent to existing more simple methods. In the analysis of dynamically loaded structures it is often assumed that the loading and the response can be modelled by stationary stochastic processes. Further, it is assumed that the structures can be modelled by non-linear systems showing hysteresis. This non-linear behaviour is essential to the design procedure from an economic and reliability point of view. In section 4 it is shown how the probability of failure of a simple bilinear oscillator can be estimated and in section 5 it is demonstrated by numerical examples how model uncertainty can be included in the calculations.

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KW - Statistical Uncertainty

KW - Model Uncertainty

KW - Bilinea Hysteretic Systems

KW - Structural Reliability

KW - Physical Uncertainty

KW - Statistical Uncertainty

KW - Model Uncertainty

M3 - Article in proceeding

SN - 3-540-13185-X

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BT - System Modelling and Optimization

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PB - Springer

ER -

Sørensen JD, Thoft-Christensen P. Model Uncertainty for Bilinear Hysteretic Systems. I Thoft-Christensen P, red., System Modelling and Optimization : Proceedings of the 11th IFIP Conference. Springer. 1984. s. 585-594. (Lecture Notes in Control and Information Sciences, Bind 59).